Also the case of ρ and ρ* being equivalent representations is exactly the one in which the functional equation has the same L-function on each side.

The Cyrillic and Latin alphabets are shown below with their equivalent representations in the IPA.

The Coxian distribution is extremely important as any acyclic phase-type distribution has an equivalent Coxian representation.

The difference is only at the level of the concrete syntax, since these three versions are equivalent representations of the same abstract syntax tree.

Vasile Hutopila's paintings are a serene representation, a victory of the aesthetic truth, equivalent to the humanist love of the universe.

A functionally equivalent representation in multilevel can be:

There are three equivalent representations commonly used in two-dimensional hyperbolic geometry.

Can the representation easily be transformed (e.g. by Vocabulary-based transformation) into an equivalent representation so that semantic equivalence is ensured?

For example, the following are equivalent representations of the same value in a characteristic 2 finite field:

To ensure that the transformed system is an equivalent representation of the original system, the transformation must be a diffeomorphism.